Average work in a cycle.—The key results we present in this Letter can be viewed as a consequence of two essential features of our model, which were previosuly discussed in Refs. [1]}, [2]}, [3]}, [4]}. First, in the stable stationary regime, the driving field, \(\mathcal {S}\)  and \(\mathcal {E}\)  exchange packets of energy with values given by \(k \hbar \omega _{d}\)  (from now on \(k\)  will always be a positive integer). Second, only two processes are relevant in this regime: (i) non-resonant processes that involve environmental modes with frequencies that add up to a multiple of \(\omega _{d}\) ; and (ii) resonant processes, involving modes with frequencies whose difference is a multiple of \(\omega _{d}\) . As a consequence, \(\Delta \mathcal {Q}\) , which is constant in the stationary regime, can be expressed as the sum of two terms, each one of which arrising from one of the above processes: \(\Delta \mathcal {Q} = \Delta \mathcal {Q}^{NR} + \Delta \mathcal {Q}^{R}\) . Therefore, the average work done on \(\mathcal {S}\)  in a cycle can be expressed as
\(\bar{W}_{\mathcal {S}} = \Delta \mathcal {Q}^{NR} + \Delta \mathcal {Q}^{R}.\) 
